This is one type of green roof system. The layers shown in this photo can be used to support a sedum type (extensive) green roof. Be aware that there are other approaches to the green roof "sandwich".
Here, a felt wicking layer (white material) sits on top of a moisture retention layer (gray molded cups). Water in these cups is wicked up into a soil layer supporting growth of low water using sedum plants.
You might think of this as a form of sub-irrigation. As you can see, however, the moisture retention ("egg cups") layer provides only a small reservoir of water. This isn't meant to be a sub-irrigation system to support larger plants such as vegetables.
Low or no-maintenance is the goal of a sedum (extensive) green roof. It relies on natural rainfall rather than irrigation and inhibits rainwater runoff into the city sewer system.
Most of the green roofs I discuss here on this blog are called intensive green roofs. These green roofs require irrigation to support larger plants such as vegetables. Hose watering and drip irrigation are most widely used now.
However, as our education improves and information becomes more widely available, I believe that sub-irrigated boxes, buckets and beds will become the most favored approach. It is important to understand that this is dependent on the ability of the roof to support the additional weight of these planters.
I'm referring to the type of vegetable garden that would cover a significant area of the roof. A few EarthBox or sub-irrigated bucket type planters are unlikely to cause a problem on any roof.
It is imperative, however, to get a structural engineering report if you're planning to install many container plants with human traffic. If in doubt, get an engineering report!